Question: Rewrite as a simplified fraction. ${1.8\overline{52} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1852.5252...\\ 10x &= 18.5252...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1834}$ ${x = \dfrac{1834}{990}} $ ${x = \dfrac{917}{495}} \text{or} {1 \dfrac{422}{495}}$